Discriminant and cluster analysis for Gaussian stationary processes: local linear fitting approach

This article is concerned with discrimination and clustering of Gaussian stationary processes. The problem of classifying a realization X n  = (X 1, …, X n ) t from a linear Gaussian process X into one of two categories described by their spectral densities f 1 (λ) and f 2 (λ) is considered first. A discrimination rule based on a general disparity measure between every f i (λ), i = 1, 2, and a nonparametric spectral density estimator fˆ n (λ) is studied when local polynomial techniques are used to obtain fˆ n (λ). In particular, three different local linear smoothers are considered. The discriminant statistic proposed here provides a consistent classification criterion for all three smoothers in the sense that the misclassification probabilities tend to zero. A simulation study is performed to confirm in practice the good theoretical behavior of the discriminant rule and to compare the influence of the different smoothers. The disparity measure is also used to carry out cluster analysis of time series and some examples are presented and compared with previous works.

[1]  Robert H. Shumway,et al.  Discrimination and Clustering for Multivariate Time Series , 1998 .

[2]  W. Liggett On the Asymptotic Optimality of Spectral Analysis for Testing Hypotheses About Time Series , 1971 .

[3]  G. W. Teuscher,et al.  Prediction and control. , 1996, ASDC journal of dentistry for children.

[4]  R. Shumway,et al.  Linear Discriminant Functions for Stationary Time Series , 1974 .

[5]  Masanobu Taniguchi,et al.  Nonparametric approach for discriminant analysis in time series , 1995 .

[6]  柿沢 佳秀,et al.  Asymptotic theory of statistical inference for time series , 2000 .

[7]  D. Tjøstheim Autoregressive Representation of Seismic P-wave Signals with an Application to the Problem of Short-Period Discriminants , 1975 .

[8]  David S. Stoffer,et al.  Time series analysis and its applications , 2000 .

[9]  D. Piccolo A DISTANCE MEASURE FOR CLASSIFYING ARIMA MODELS , 1990 .

[10]  R. Shumway,et al.  An examination of some new and classical short period discriminants. Technical report , 1974 .

[11]  Elias Masry,et al.  Multivariate regression estimation: local polynomial fitting for time series , 1997 .

[12]  Gerda Claeskens,et al.  Bootstrap confidence bands for regression curves and their derivatives , 2003 .

[13]  W Gersch,et al.  Automatic classification of electroencephalograms: Kullback-Leibler nearest neighbor rules. , 1979, Science.

[14]  H. Tong,et al.  Cluster of time series models: an example , 1990 .

[15]  Elizabeth Ann Maharaj,et al.  A SIGNIFICANCE TEST FOR CLASSIFYING ARMA MODELS , 1996 .

[16]  Rahim Chinipardaz,et al.  Discrimination of AR, MA and ARMA time series models , 1996 .

[17]  Jianqing Fan,et al.  Local polynomial modelling and its applications , 1994 .

[18]  G. R. Dargahi-Noubary,et al.  Disoominkfrcn between gaussian time series based on their spectral differences , 1992 .

[19]  D. B. Preston Spectral Analysis and Time Series , 1983 .

[20]  Masanobu Taniguchi,et al.  DISCRIMINANT ANALYSIS FOR STATIONARY VECTOR TIME SERIES , 1994 .

[21]  Frédéric Ferraty,et al.  Curves discrimination: a nonparametric functional approach , 2003, Comput. Stat. Data Anal..

[22]  Chris Chatfield,et al.  Introduction to Statistical Time Series. , 1976 .

[23]  J. Alagón SPECTRAL DISCRIMINATION FOR TWO GROUPS OF TIME SERIES , 1989 .

[24]  R. H. Shumway,et al.  1 Discriminant analysis for time series , 1982, Classification, Pattern Recognition and Reduction of Dimensionality.

[25]  Y. Kakizawa Discriminant analysis for non-gaussian vector stationary processes , 1996 .

[26]  Elizabeth Ann Maharaj,et al.  Cluster of Time Series , 2000, J. Classif..

[27]  M. Francisco-Fernández,et al.  On the Uniform Strong Consistency of Local Polynomial Regression Under Dependence Conditions , 2003 .

[28]  A.S. Gevins,et al.  Automated analysis of the electrical activity of the human brain (EEG): A progress report , 1975, Proceedings of the IEEE.

[29]  G. P. King,et al.  Using cluster analysis to classify time series , 1992 .

[30]  Jack Capon,et al.  An Asymptotic Simultaneous Diagonalization Procedure for Pattern Recognition , 1965, Inf. Control..